If $R$ is the set of all real numbers, what do the cartesian products $R \times R$ and $R \times R \times R$ represent?
The Cartesian product $R \times R$ represents the set $R \times R =\{(x, y): x, y \in R \}$ which represents the coordinates of all the points in two dimensional space and the cartesian product $R \times R \times R$ represents the set $R \times R \times R =\{(x, y, z): x, y, z \in R \}$ which represents the coordinates of all the points in three-dimensional space.
Let $A=\{1,2\}, B=\{1,2,3,4\}, C=\{5,6\}$ and $D=\{5,6,7,8\} .$ Verify that
$A \times(B \cap C)=(A \times B) \cap(A \times C)$
The solution set of $8x \equiv 6(\bmod 14),\,x \in Z$, are
If $\left(\frac{x}{3}+1, y-\frac{2}{3}\right)=\left(\frac{5}{3}, \frac{1}{3}\right),$ find the values of $x$ and $y$
State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly.
If $A$ and $B$ are non-empty sets, then $A \times B$ is a non-empty set of ordered pairs $(x, y)$ such that $x \in A$ and $y \in B.$
State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly.
If $A=\{1,2\}, B=\{3,4\},$ then $A \times\{B \cap \varnothing\}=\varnothing$